1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The potential energy of a $$1$$ $$kg$$ particle free to move along the $$x$$-axis is given by $$V\left( x \right) = \left( {{{{x^4}} \over 4} - {{{x^2}} \over 2}} \right)J$$.

The total mechanical energy of the particle is $$2J.$$ Then, the maximum speed (in $$m/s$$) is

A
$${3 \over {\sqrt 2 }}$$
B
$${\sqrt 2 }$$
C
$${1 \over {\sqrt 2 }}$$
D
$$2$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A bomb of mass $$16kg$$ at rest explodes into two pieces of masses $$4$$ $$kg$$ and $$12$$ $$kg.$$ The velocity of the $$12$$ $$kg$$ mass is $$4\,\,m{s^{ - 1}}.$$ The kinetic energy of the other mass is
A
$$144$$ $$J$$
B
$$288$$ $$J$$
C
$$192$$ $$J$$
D
$$96$$ $$J$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass through a distance $$d,$$ by what distance should the second particle is moved, so as to keep the center of mass at the same position?
A
$${{{m_2}} \over {{m_1}}}\,\,d$$
B
$${{{m_1}} \over {{m_1} + {m_2}}}d$$
C
$${{{m_1}} \over {{m_2}}}d$$
D
$$d$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega $$. Two objects each of mass $$M$$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $$\omega ' = $$
A
$${{\omega \left( {m + 2M} \right)} \over m}$$
B
$${{\omega \left( {m - 2M} \right)} \over {\left( {m + 2M} \right)}}$$
C
$${{\omega m} \over {\left( {m + M} \right)}}$$
D
$${{\omega m} \over {\left( {m + 2M} \right)}}$$
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